Why do a lot of American states have panhandles?

Question

I heard that the surveyors made a mistake in the arithmetic. Is this right?

Answer 1

panhandle is an informal geographic term for an elongated tail-like protrusion of a geo-political entity, such as a subnational entity or a sovereign state. The term derives from the analogous part of a cooking pan and its use is generally confined to the United States. A panhandle is similar to a peninsula in shape, but unlike a peninsula it is not surrounded by water on three sides and connected to a geographical mainland. Instead, a panhandle is delimited by a land border on at least two sides and extends out from the larger geographical body of the administrative unit. The panhandle shape is the result of arbitrarily drawn international or subnational boundaries, although the location of some administrative borders takes into account other considerations such as economic ties or topography. In the United States, a protrusion with a less elongated shape is informally called a bootheel.

Outside of the United States, the term is not in common usage, with the arguable exception of the nearby New Brunswick Panhandle. Nonetheless, some people would describe the following characteristic territorial protrusions elsewhere as a corridor or an arm extending into an administratively different territory. Such shapes of territory can be a result of linguistic (or ethnic) lines, in addition to geographic features and other reasons.

Answer 2

That's just how things turned out.  The only panhandle that's specifically due to a surveying mistake is Idaho's.  When the Montana territory was carved out from Idaho Territory, the plan was to have everything west of the Continental Divide be in Idaho.  However, for part of the way the surveyors followed the wrong mountain range, thus putting a fair-sized chunk of land into Montana that was supposed to be in Idaho.  If they'd done the job right from start to finish, Montana would be smaller and Idaho wouldn't have a panhandle.